# RC Circuit Time Constant Calculator

Calculate RC circuit time constant, charging voltages at 1τ through 5τ, and time to 99% charge. Enter resistance and capacitance for instant results.

## What this calculates

An RC circuit's time constant τ = RC determines how quickly a capacitor charges or discharges through a resistor. After one time constant, the capacitor reaches about 63.2% of the supply voltage. This calculator shows the time constant and capacitor voltage at key intervals.

## Inputs

- **Resistance** (Ω) — min 0 — Resistance in ohms.
- **Capacitance** (μF) — min 0 — Capacitance in microfarads.
- **Supply Voltage** (V) — min 0 — DC supply voltage applied to the RC circuit.

## Outputs

- **Time Constant (τ)** (ms) — τ = R × C. Time for the capacitor to reach ~63.2% of supply voltage.
- **Voltage at 1τ** (V) — Capacitor voltage after 1 time constant (~63.2%).
- **Voltage at 2τ** (V) — Capacitor voltage after 2 time constants (~86.5%).
- **Voltage at 3τ** (V) — Capacitor voltage after 3 time constants (~95.0%).
- **Voltage at 5τ** (V) — Capacitor voltage after 5 time constants (~99.3%).
- **Charge Time to 99%** (ms) — Time to reach 99% of supply voltage (≈ 4.605τ).

## Details

The RC time constant (τ = RC) is the fundamental parameter governing the transient response of a resistor-capacitor circuit. During charging, the capacitor voltage follows the exponential curve V(t) = V0(1 - e-t/τ), asymptotically approaching the supply voltage. During discharging, it follows V(t) = V0e-t/τ.

Key milestones: after 1τ the capacitor reaches 63.2% of its final value; after 3τ it reaches 95.0%; and after 5τ it reaches 99.3%, which is considered "fully charged" in most practical applications. The rule of thumb is that an RC circuit settles to its final state within 5 time constants.

RC circuits are ubiquitous in electronics. They serve as low-pass and high-pass filters, smoothing power supply ripple, debouncing switches, creating time delays, and coupling AC signals between amplifier stages. The cutoff frequency of an RC filter is fc = 1/(2πRC), directly related to the time constant.

## Frequently Asked Questions

**Q: What does the time constant τ represent?**

A: The time constant τ = RC is the time it takes for the capacitor voltage to reach approximately 63.2% of its final value during charging, or to decay to 36.8% during discharging.

**Q: How long does it take to fully charge a capacitor?**

A: Theoretically, a capacitor never fully charges (it approaches the supply voltage asymptotically). In practice, after 5 time constants (5τ) the capacitor is at 99.3% and is considered fully charged.

**Q: What happens if I increase the resistance in an RC circuit?**

A: Increasing resistance increases the time constant, meaning the capacitor charges and discharges more slowly. The final voltage remains the same, but it takes longer to reach it.

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Source: https://vastcalc.com/calculators/technology/rc-circuit
Category: Technology
Last updated: 2026-04-21